A. A. Galt, V. N. Tyutyanov, “On the existence of <nobr>$G$</nobr>-permutable subgroups in simple sporadic groups”, Sibirsk. Mat. Zh., 2022, Volume 63, Number 4,Pages <nobr>831

This article is cited in 8 papers

On the existence of $G$-permutable subgroups in simple sporadic groups

A. A. Galt^a, V. N. Tyutyanov^b

^a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
^b Gomel Branch of International University "MITSO"

Abstract: A subgroup $A$ of a group $G$ is $G$-permutable in $G$ if for every subgroup $B\leq G$ there is $x\in G$ satisfying $AB^x=B^xA$. A subgroup $A$ is hereditarily $G$-permutable in $G$ if $A$ is $E$-permutable in every subgroup $E$ of $G$ which includes $A$. The Kourovka Notebook contains Problem 17.112: Which finite nonabelian simple groups $G$ possess a proper (hereditarily) $G$-permutable subgroup? We answer the question for simple sporadic groups.

Keywords: simple sporadic group, $G$-permutable subgroup, hereditarily $G$-permutable subgroup.

UDC: 512.542

MSC: 35R30

Received: 11.11.2021
Revised: 18.03.2022
Accepted: 15.04.2022

DOI: 10.33048/smzh.2022.63.409